One, with sculpted arms and torso, is bug-eyed and charming, hands perched on enormous clay hips that expand outward, creating the bone chamber. Another seems whimsical, circular eyes agape, as if surprised at what life has come to. A third, sporting a mustache, avuncularly perches atop a clay pot.

Is this how death itself was imagined or how particular individuals were recalled? In the myths and relics of ancient peoples, we are more used to death’s having fierce power, with burial arrangements that invoke earthly glory. Nothing like that here. These were decorous repositories for bones that had already been buried and disinterred and were finally being put to rest; they make death seem almost collegial. What kind of societies created these burial pots between 4500 B.C. and 3600 B.C., placing them in caves and subterranean chambers in a region that now includes parts of Israel and Jordan?

That is a mystery that arises again and again as we make our way through these two galleries with 157 objects from the Israel Museum, including finely wrought copper scepters, an olive-wood bow intentionally snapped in two and interred with its archer, frail wraiths of linen uncannily preserved for millenniums, basalt statuettes and ritual objects of unknown purpose.

The vision of humanity we see portrayed here doesn’t seem to fit what we expect — not just in the treatment of death, but in the evocation of the living. It is as if we had stumbled on caches of private objects — personal, individual, quirky — rather than on collections of public or sacred relics. Here is a miniature figurine, for example, a head carved of ivory and crowned with a twisting headdress; the detail is minimal, but the facial expression is somber and unmistakably introspective.

There are two clay libation vessels, found in the ruins of a temple complex in the Israeli Negev, seemingly representing fertility deities: A woman with prominent genitalia carries a churn used for making butter on her head; a ram god with carved face and nostrils, covered with a geometric pattern suggesting a blanket, bears three vessels on his back. These figures surprise us as much as the ossuaries.

In other ancient societies, particularly in agricultural lands of uncertain harvest, we are used to seeing deities as unpredictable forces to be placated; fertility gods would have immense importance as the guarantors of life. But these gods are not terrifying or otherworldly in the least. They are part of the everyday. A spirit of intimacy and familiarity seems to govern the divine as well as the dead. How do we make sense of this?

The puzzle is that when we turn to what is actually understood about these societies, it almost seems to point in the opposite direction — not toward the personal, but toward the institutional and social — and the different realms aren’t always easy to reconcile. Almost everything known or guessed about these artifacts and their times developed during the last 50 years. In 1961, an archaeologist was rappelling off the cliffs above the Dead Sea and discovered what would become known as the Cave of the Treasure. It included 429 objects made from copper, ivory and stone, wrapped in a straw mat. In the invaluable exhibition catalog (published by Princeton University Press), one of the show’s curators, Daniel M. Master, an archaeologist at Wheaton College, calls the cave one of the great hoards of antiquity.

Discoveries continued, with related artifacts coming to light in the southern Israeli desert, in the Golan Heights and in Jordan. The material did much to fill in a vaguely understood link between the Neolithic era, when animals were domesticated, and the Bronze Age (3600-1200 B.C.). It was characterized as Chalcolithic, a name invoking both copper and stone.

On the face of it, the copper objects on display here (aside from a highly ornamented crown) might even be overlooked as less intriguing than the ceramic ossuaries, even though we are told that they are “far more elaborate” than any others from the same period. The most imposing examples are scepters with spiral copper ridges, decorated with elegantly shaped discs and copper balls seemingly wound in metal.

But scepters, of course, are meant to proclaim power. And that is crucial to one influential interpretation of these discoveries. In the catalog, the archaeologist Thomas E. Levy points out that the copper ore used to create these scepters came from a greater distance than the copper of some other artifacts found, and that their complex castings were also created using sophisticated wax molds. (Beeswax may have been used, indicating the beginnings of horticulture.) Mr. Levy estimates that it might have taken 50 hours to process the ore, and then cast and finish a single simple copper ax.

These objects, in this view, were associated with a newly forming social elite. So, it seems, were the ossuaries, which were, after all, selective in their reinterment of bones. These Chalcolithic finds might even offer the earliest signs of a proto-modern, hierarchical society taking shape. The manufacture of such copper objects required territorial control and trade; it demanded the mastery of specialized crafts and techniques; and the process required the exercise of wealth and power. Early temple complexes have also been excavated, hinting at a priesthood. There is evidence of population growth during this era, along with the beginnings of village life.

A similar history is told at the imposing, recently reimagined galleries of the Israel Museum, using these same Chalcolithic objects, as well as many others. (One of that museum’s curators, Osnat Misch-Brandl, is an organizer of the New York University show, as are Michael Sebbane of the Israel Antiquities Authority; Mr. Master; and the N.Y.U. institute’s director, Jennifer Y. Chi). The New York exhibition, of course, is far less sweeping, but it also lets us see the mysteries more clearly.

Because here we have the relics of hundreds of years of human settlement during an era of great technological and social change: an era in which specialization and hierarchical organization evolved. Yet what do we see in the artifacts themselves? Not those great transformative forces, not demonstrations of power or powerlessness, not an invocation of divine forces demanding submission or sacrifice — but hints of individuality, introspection, personality and the immanent ordinariness of divinities.

This is, to me, remarkable. Were these objects expressions of confidence by the elites — that they were just like the divinities walking among them? Or was there so widespread a sense of cultic intimacy in these early years of hierarchy that even the elites would have felt some deference, some limits to their power as they commanded their metallurgical miracles?

We can only speculate. But Mr. Master points out that the Chalcolithic “was a brief moment when the Southern Levant was at the forefront of human technological and artistic development.” Then, almost 6,000 years ago, these cultures began to fade, eclipsed by the growth of Egypt and Mesopotamia, the great looming civilizations of the Bronze Age, which had little interest in intimate visions left interred in Judean caves.